x^2+18x+81=33

Solution for x^2+18x+81=33 equation:

x^2+18x+81=33

We move all terms to the left:

x^2+18x+81-(33)=0

We add all the numbers together, and all the variables

x^2+18x+48=0

a = 1; b = 18; c = +48;
Δ = b2-4ac
Δ = 182-4·1·48
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{33}}{2*1}=\frac{-18-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{33}}{2*1}=\frac{-18+2\sqrt{33}}{2}
$